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Chapter 8: Problem 24

(a) Does the lattice energy of an ionic solid increase or decrease (i) as the charges of the ions increase, (ii) as the sizes of the ions increase? (b) Arrange the following substances not listed in Table \(8.2\) according to their expected lattice energies, listing them from lowest lattice energy to the highest: \(\mathrm{MgS}\), KI, GaN, LiBr.

Short Answer

Expert verified
(a) (i) As the charges of the ions increase, the lattice energy of an ionic solid increases. (ii) As the sizes of the ions increase, the lattice energy of an ionic solid decreases. (b) The substances arranged in order of increasing lattice energy are: KI, LiBr, MgS, GaN.

Step by step solution

01

Understanding Lattice Energy

Lattice energy is the energy required to separate a solid ionic compound into its constituent ions. It can be described using the following formula: \(U = k \frac{Q_1 Q_2}{r}\) where, - U is the lattice energy - k is the electrostatic constant - Q_1 and Q_2 are the charges of the ions involved - r is the distance between the ions (which is related to ion size) Now let's analyze the exercise step by step:
02

Part (a): Impact of Ion Charge on Lattice Energy

(i) As the charge of the ions increases, the lattice energy will be affected according to the formula. Let's look at the charges term (Q_1 * Q_2). If the charges of the ions increase, then the product of the charges (Q_1 * Q_2) will also increase, leading to an increase in lattice energy (U): \(U = k \frac{Q_1 Q_2}{r}\) Therefore, as the charges of the ions increase, the lattice energy of an ionic solid increases.
03

Part (a): Impact of Ion Size on Lattice Energy

(ii) As the size of the ions increases, the distance between the ions (r) will also increase. The lattice energy will be affected according to the formula. If r increases, then the lattice energy (U) will decrease: \(U = k \frac{Q_1 Q_2}{r}\) Therefore, as the sizes of the ions increase, the lattice energy of an ionic solid decreases.
04

Part (b): Arranging Substances by Lattice Energy

Now we need to arrange the following substances according to their expected lattice energies: MgS, KI, GaN, LiBr. We'll consider two factors for this: (1) the product of the ion charges, as higher charges lead to higher lattice energies, and (2) the size of the ions, as larger ions lead to lower lattice energies. Here's a summary of the substances involved: - MgS: Magnesium (Mg) has a charge of +2, and Sulfide (S) has a charge of -2. The product of the charges is 4, and the ions have medium size. - KI: Potassium (K) has a charge of +1, and Iodide (I) has a charge of -1. The product of the charges is 1, and the ions are large. - GaN: Gallium (Ga) has a charge of +3, and Nitride (N) has a charge of -3. The product of the charges is 9, and the ions have small size. - LiBr: Lithium (Li) has a charge of +1, and Bromide (Br) has a charge of -1. The product of the charges is 1, and the ions have medium size. Now we can arrange the substances based on these factors: 1) Lowest lattice energy: KI (lowest product of ion charges and largest size) 2) LiBr (low product of ion charges and medium size) 3) MgS (higher product of ion charges and medium size) 4) Highest lattice energy: GaN (highest product of ion charges and smallest size) The arranged order from lowest lattice energy to highest is as follows: KI, LiBr, MgS, GaN.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Ionic Compounds
Ionic compounds are substances composed of positively and negatively charged ions that are held together by strong electrostatic forces known as ionic bonds. These compounds typically form when a metal donates one or more electrons to a non-metal, creating a stable electron configuration for both ions involved.

This transfer of electrons results in a cation, a positively charged ion, and an anion, a negatively charged ion. The resulting compound is neutral overall but consists of differently charged ions arranged in a regular, repeating pattern, or lattice structure. For example, table salt (sodium chloride) is an ionic compound where each sodium ion (Na+) is surrounded by chloride ions (Cl-) and vice versa, creating a stable, crystalline solid.
Impact of Ion Charge on Lattice Energy
The charge of an ion plays a significant role in determining the lattice energy of an ionic compound. Lattice energy is basically the energy required to separate an ionic solid into its gaseous ions.

According to Coulomb's Law, the force of attraction or repulsion between two charged particles is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. This principle translates to lattice energy as well. As the charge of the ions increases, the force of attraction between them becomes stronger, thus requiring more energy to break the ionic bonds. Therefore, an ionic compound with ions of higher charges will have a greater lattice energy.
The Influence of Ion Size on Lattice Energy
Ion size, or the distance between the nuclei of the ions, is another crucial factor affecting lattice energy. Larger ions have a more extended electron cloud, which can lead to increased shielding and a reduction in attraction forces between ions. Consequently, increasing ion size corresponds to a decrease in lattice energy.

In practical terms, when comparing the lattice energy of different ionic compounds, it's important to note that smaller ions tend to be more tightly packed within a lattice structure, which means the distance between their centers (the ionic radii) is smaller, resulting in stronger attraction and higher lattice energy. Hence, compounds with smaller ions typically demonstrate higher lattice energies compared to those made up of larger ions.

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Most popular questions from this chapter

One scale for electronegativity is based on the concept that the electronegativity of any atom is proportional to the ionization energy of the atom minus its electron affinity: electronegativity \(=k(I-E A)\), where \(k\) is a proportionality constant. (a) How does this definition explain why the electronegativity of \(\mathrm{F}\) is greater than that of \(\mathrm{Cl}\) even though \(\mathrm{Cl}\) has the greater electron affinity? (b) Why are both ionization energy and electron affinity relevant to the notion of electronegativity? (c) By using data in Chapter 7 , determine the value of \(k\) that would lead to an electronegativity of \(4.0\) for \(F\) under this definition. (d) Use your result from part (c) to determine the electronegativities of \(\mathrm{Cl}\) and \(\mathrm{O}\) using this scale. (e) Another scale for electronegativity defines electronegativity as the average of an atom's first ionization energy and its electron affinity. Using this scale, calculate the electronegativities for the halogens, and scale them so fluorine has an electronegativity of 4.0. On this scale, what is Br's electronegativity?

List the individual steps used in constructing a Born-Haber cycle for the formation of \(\mathrm{BaI}_{2}\) from the elements. Which of the steps would you expect to be exothermic?

(a) Construct a Lewis structure for hydrogen peroxide, \(\mathrm{H}_{2} \mathrm{O}_{2}\), in which each atom achieves an octet of electrons. (b) How many bonding electrons are between the two oxygen atoms? (c) Do you expect the \(\mathrm{O}-\mathrm{O}\) bond in \(\mathrm{H}_{2} \mathrm{O}_{2}\) to be longer or shorter than the \(\mathrm{O}-\mathrm{O}\) bond in \(\mathrm{O}_{2}\) ? Explain.

Write Lewis structures for the following: (a) \(\mathrm{H}_{2} \mathrm{CO}\) (both \(\mathrm{H}\) atoms are bonded to \(\mathrm{C}\) ), (b) \(\mathrm{H}_{2} \mathrm{O}_{2}\), (c) \(\mathrm{C}_{2} \mathrm{~F}_{6}\) (contains a \(\mathrm{C}-\mathrm{C}\) bond), (d) \(\mathrm{AsO}_{3}{ }^{3-}\), (e) \(\mathrm{H}_{2} \mathrm{SO}_{3}\) ( \(\mathrm{H}\) is bonded to \(\mathrm{O}\) ), (f) \(\mathrm{NH}_{2} \mathrm{Cl}\).

Write electron configurations for the following ions, and determine which have noble-gas configurations: (a) \(\mathrm{Cd}^{2+}\), (b) \(\mathrm{P}^{3-}\), (c) \(\mathrm{Zr}^{4+}\), (d) \(\mathrm{Ru}^{3+}\), (e) \(\mathrm{As}^{3-}\), (f) \(\mathrm{Ag}^{+}\).
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